Given: RT || SP, RQ ≅ QP, RP bisects ST at Q
Prove: ΔRQT ≅ ΔPQS

Triangles R Q T and P Q S are connected at point Q. Lines R T and S P are parallel. The lengths of lines R Q and Q P are congruent.
Tamir is working to prove the triangles congruent using SAS. After stating the given information, he states that TQ ≅ QS by the definition of segment bisector. Now he wants to state that ∠RQT ≅ ∠PQS. Which reason should he use?

alternate interior angles theorem
corresponding angles theorem
linear pair postulate
vertical angles theorem

Answer:

20/39.

Step-by-step explanation:

There are a total of 13 students.

Prob(Boy is selected) = 8/13

Prob(Girl is then selected) = 5/12

So probability ( Boy selected then a girl)  = 8/13 * 5/12 = 10/39

- and the probability of Girl then a boy selected is also  10/39

So the required probability = 2 * 10/39

= 20/39.

From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.

So, slope of the line (m) passing through the points (a, b) and (c, d) is

m = d - b/ c - a

m = 4 - 3 / 1 - 0 = 1/1 = 1

Also, line makes an intercept of 3 units in positive direction of y - axis.

So, c = 3

y = mx + c

y = 1 × x + 3

We know, Equation of line passing through the points (a,b) and (c, d) is given by

y - b = d - b / c - a (x - a)

a = 0

b = 3

c = 1

d = 4

y - 3 = 4 - 3 /1 - 0 ( x - 0 )

y - 3 = 1/1 ( x - 0 )

y - 3 = x

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

Equation of line passing through the point (a, b) having slope m isy - b = m(x - a)

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

Equation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.

Answer:

1.88 m^2/min to the nearest hundredth.

Step-by-step explanation:

Area = π r^2

Using Calculus notation:

dA/dr = 2π r

dr/dt = 0.25  (given)

So the rate of change of area

dA/dt = dA/dr * dr/dt

So when r = 1.2

dA/dt = 2 π * 1.2 * 0.25

= 0.6π  m^2/min.

= 1.88 m^2/min to the nearest hundredth.

Answer:

the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so  we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.

Step-by-step explanation: hopefully that is the correct and have a great day.

Answer:

b

Step-by-step explanation:

[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]

[tex] = \frac{50}{5} \\ [/tex]

Change into lowest term

[tex]10...[/tex]

Answer:

0,5

Step-by-step explanation:

Answer:

b = 5 ± √5 / 5

Step-by-step explanation:

Given :

Subtract 10b from both sides :

Splitting the middle term :

Answer:

42 units ^2

Step-by-step explanation:

Break in to a top triangle   a middle rectangle and a bottom triangle

area =   1/2 7 *2      +    4 * 7        1/2 * 2 * 7 = 42 units ^2

Answer:

270

Step-by-step explanation:

 x = k/y     This is an inverse relationship with k = constant of proportion (or variation)

-9 = k/(-30)

k = -9  *  -30 = 270

Answer:

Constant of variation  = 270.

Step-by-step explanation:

y = k/x

-30 = k / -9

k = -30 * -9

k = 270

Answer:  6 inches equals 0.16666667 yards, or about 0.2 yards.

Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.

6/36 = 0.16666667

The answer is 0.16666667 yards, or about 0.2 yards.

Answer:

  (x, y) = (12, 15)

Step-by-step explanation:

The given expression for y suggests that using substitution would be a good choice for the method of solution.

__

  x +(x +3) = 27 . . . . substitute for y using the second equation

  2x = 24 . . . . . . . subtract 3

  x = 12 . . . . . . . divide by 2

  y = 12 +3 = 15 . . . . use the second equation to find y

The solution is (x, y) = (12, 15).

The number  2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

= 2√5×3√6

= 6√30

= √1080 = 32.863353450309965

The number is irrational.

= √42/√168

= 1/2

The number is rational.

= 5(4√5 - 3√5)

= 5√5

= √125 = 11.180339887498949

The above number is irrational.

= √64/32

= 1/4

The above number is rational.

= (5√3—√3)/2√3

= 2

The above number is rational.

Similarly, we can find whether a number is irrational or rational

Thus, the number  2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.

Learn more about the irrational number here:

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Answers:

BD = 6

AC = 7.5

=================================================

Work Shown:

BD/BA = BE/BC

x/9 = 4/6

6x = 9*4

6x = 36

x = 36/6

x = 6

BD = 6

---------

DE/AC = BE/BC

5/y = 4/6

5*6 = y*4

30 = 4y

4y = 30

y = 30/4

y = 7.25

AC = 7.5

Answer:

243 in²

Step-by-step explanation:

Diameter = 18 in

Radius ( r ) = Diameter / 2 = 18 / 2

r = 9 in

π = 3

To find : Area of circle ( A )

Formula : -

A = πr²

A = 3 x 9²

   = 3 x 9 x 9

A = 243 in²

Answer:

Quadrant IV is always in the bottom right corner.

Answer:

  800 ft²

Step-by-step explanation:

The total surface area of a square-base pyramid is given by the formula ...

  A = s(s +2h) . . . . . . where s is the side length, h is the face slant height

In this problem, we need to find the slant height of a face in order to use this formula.

__

The distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.

The Pythagorean theorem is used to find the hypotenuse of that triangle:

  c² = a² +b² . . . . square of hypotenuse = sum of squares of legs

  c² = 15² +8² = 225 +64 = 289

  c = √289 = 17

The slant height of a face of the pyramid is 17 ft.

The area formula tells us the total surface area is ...

  A = s(s +2h)

  A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)

  A = 800 ft²

The total surface area is 800 square feet.

Answer:

  p(x) = x⁴ -7x³ +59x² -343x +490

Step-by-step explanation:

Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.

__

The given roots mean the polynomial can be written in factored form as ...

  p(x) = (x -2)(x -5)(x -7i)(x -(-7i))

We can combine multiply these factors together to simplify the polynomial.

  p(x) = (x² -7x +10)(x² +49)

  p(x) = x⁴ -7x³ +59x² -343x +490

_____

Additional comment

Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.

  a² -b² = (a -b)(a +b)

  (x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)

Answer:

(4+5) ÷ 3 + 6 x 5

Step-by-step explanation:

pemdas

Answer:

B

Step-by-step explanation:

1.

- 9 < 2x + 1

- 10 < 2x

X > - 5

2.

2x + 1 < 5

2x < 4

X < 2

Pull out a factor of 1/n from the summand and the result follows.

[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]

Answer:

d=6 & p=13

Step-by-step explanation:

1. P+d=19

×9

2. 9p +5.50d=150

×1

9p+9d=171

-

9p +5.50d=150

3.5d=21

d=6

Substituting d=6 in 1.

P+6=19

P=13

Answer:

The average mass of one coffee bag is 75kg.

Step-by-step explanation:

The lorry on its own weighs 3500kg.

If it weighs 7250kg alongside coffee bags, we can make the assumption that to find the total mass of the coffee bags, we must take the combined total and subtract the lorry's weight from it.

7250kg subtract 3500kg is 3750kg.

There are 50 coffee bags, so this is the mass of all 50.

If we want to find the mass of one coffee bag, we have to divide the mass of 50 coffee bags by 50.

3750kg divided by 50 is 75kg.

The average mass of one coffee bag is 75kg.

the amount of maturity is 254583

Answer:

C

Step-by-step explanation:

Because it's a negative, then we could assume that it is a negative correlation. And because it's closer to -1, it is a strong negative correlation.

The value -0.993 is Strong Negative correlation.

The strength and direction of two variables in a scatterplot are quantified by the correlation coefficient, or r value. It goes from one to one.

So, the value close to 1 is Strong positive correlation and close to -1 is Strong Negative correlation.

Thus, -0.993 close to -1 is Strong Negative correlation.

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The surface area of the solid is 4 + 6b

The solid consist of the following shapes:

The area of the solid is:

Area = Area of square + 4 * area of triangle

This gives

Area = 2 * 2 + 4 * 0.5 * 3 * b

Evaluate

Area = 4 + 6b

Hence, the surface area of the solid is 4 + 6b

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The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively

The event A is given as:

A : Sum greater than 6

In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes

This means that:

P(A) = 21/36

Simplify

P(A) = 7/12

The event B is given as:

B : Sum is divisible by 2

In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes

This means that:

P(B) = 18/36

Simplify

P(B) = 1/2

Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively

Read more about probability at:

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